Multigrid methods for stabilized nonconforming finite elements for incompressible flow involving the deformation tensor formulation

S. Turek; A. Ouazzi; R. Schmachtel

doi:10.1515/JNMA.2002.235

Published by De Gruyter November 15, 2010

Multigrid methods for stabilized nonconforming finite elements for incompressible flow involving the deformation tensor formulation

S. Turek , A. Ouazzi and R. Schmachtel

From the journal Journal of Numerical Mathematics

https://doi.org/10.1515/JNMA.2002.235

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Abstract

Edge-oriented stabilization methods in the framework of discontinuous Galerkin approaches have been recently proposed by Brenner [Korn's inequalities for piecewise H¹ vector fields, University of South Carolina, 2002] and particularly by Hansbo and Larson [A simple nonconforming bilinear element for the elasticity problem, CIMNE, 2001] for nonconforming finite element discretizations to satisfy a discrete Korn's inequality. We develop and analyse corresponding multigrid components in combination with local Pressure-Schur-Complement methods and give numerical examples for incompressible newtonian and non-newtonian fluids.

Keywords:: Multigrid; nonconforming FEM; discontinuous Galerkin; incompressible CFD

Received: 2002-04-30

Revised: 2002-08-01

Published Online: 2010-11-15

Published in Print: 2002-September